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Estimating the Link Function in Multinomial Response Models under Endogeneity and Quadratic Loss

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  • Judge, George G.
  • Mittelhammer, Ron C

Abstract

This paper considers estimation and inference for the multinomial response model in the case where endogenous variables are arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. A data based shrinkage estimator that seeks an optimal combination of estimators and results in superior risk performance under quadratic loss is also developed.

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Bibliographic Info

Paper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt4422n50w.

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Date of creation: 03 Feb 2004
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Handle: RePEc:cdl:agrebk:qt4422n50w

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Keywords: multinomial process; endogeneity; empirical likelihood procedures; quadratic loss; semiparametric estimation and inference; data dependent shrinkage; asymptotic and finite sample risk;

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References

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  1. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, number emetr2, Spring.
  2. Mittelhammer, Ronald C. & Judge, George G. & Schoenberg, Ron, 2003. "Empirical evidence concerning the finite sample performance of El-type structural equation estimation and inference methods," CUDARE Working Paper Series 945, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  3. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
  4. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
  5. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
  6. Hong, Han & Tamer, Elie, 2003. "Endogenous binary choice model with median restrictions," Economics Letters, Elsevier, vol. 80(2), pages 219-225, August.
  7. Mittelhammer, Ron C. & Judge, George G., 2005. "Combining estimators to improve structural model estimation and inference under quadratic loss," Journal of Econometrics, Elsevier, vol. 128(1), pages 1-29, September.
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Citations

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Cited by:
  1. Mittelhammer, Ronald C. & Judge, George G. & Miller, Douglas & Cardell, Nicholas Scott, 2005. "Minimum divergence moment based binary response models : estimation and inference," CUDARE Working Paper Series 0998, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  2. Villas-Boas, Sofia B., 2007. "Vertical relationships between manufacturers and retailers: inference with limited data," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt6gz1t778, Department of Agricultural & Resource Economics, UC Berkeley.

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